Course detail

FEM in Engineering Computations II

FSI-RNUAcad. year: 2025/2026

The course is a follow-up to basic lectures in solid mechanics, which are traditionally limited to linear problems, and introduces the basic nonlinearities. Material nonlinearity is represented by several models of plastic behaviour.
Next, contact problems, large displacement and large strain problems are presented. Although some classical solutions to selected nonlinear problems are mentioned (Hertz contact, deformation theory of plasticity), attention is given to numerical solution by the FEM. Above all, the relation between stability and convergence of numerical solution and physical interpretation of the analysed problem is thoroughly inspected in seminars.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Jindřich Petruška, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Entry knowledge

Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations.
Others: basic theory of elasticity, theory and practical knowledge of the FEM.

Rules for evaluation and completion of the course

The course-unit credit for seminars is granted under the condition of:
- active participation in seminars,
- individual preparation and presentation of a seminar project.
Final evaluation is based on the result of examination, which has a form of a written test of gained knowledge.


Attendance at practical training is obligatory. The absence (in justified cases) is compensated by additional assignments according to the instructions of the tutor.

Aims

The aim of the course is to provide students with theoretical knowledge and elementary experience with the solution of most frequent types of nonlinear
problems of solid mechanics.
Students learn how to classify basic types of nonlinear behaviour in solid mechanics, they will learn their characteristics and classical solutions for some
types of problems. They can prepare numerical computational model, solve it using some of the commercial FE systems and make a rational analysis of
typical problems with divergence of the iterative process of solution.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

G.A.Holzapfel: Nonlinear Solid Mechanics, Wiley, 2000
K.-J.Bathe: Finite Element Procedures, K.-J.Bathe, 2014
M.A.Crisfield et al.: Non-linear Finite Element Analysis of Solids and Structures, Wiley, 2012

Recommended reading

I.Něměc, M.Trcala, V.Rek: Nelineární mechanika, VUTIUM, 2018 (CS)

Classification of course in study plans

  • Programme N-IMB-P Master's

    specialization IME , 1 year of study, summer semester, compulsory
    specialization BIO , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

1. Introduction to nonlinear problems of solid mechanics
2. Incremental theory of plasticity and its implementation in FEM systems, Deformation theory of plasticity
3. Elasto-plastic bending of beams, plastic hinge and plastic collaps
4. Elasto-plastic response to cyclic loading
5. Residual stress
6. Contact problems - classical solution
7. Strategy of contact solution in FEM, characteristics of contact elements
8. Large displacement and strain - alternative formulations of strain tensors
9. Large displacement and strain - continued
10. Engineering vs. natural stress and strain, evaluation of materiál flow curve in natural coordinates
11. Stability of thin-walled structures as a nonlinear problem of mechanics
12. Explicit formulation of FEM in nonlinear problems of mechanics
13. Convergence of numerically solved nonlinear problem

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

1. Convergence of iterative solution of nonlinear problem - numerical demonstrations
2. Plasticity in FEM - solution of selected tasks
3. Plasticity in FEM - solution of selected tasks
4. Start of seminar project
5. Plastic collaps
6. Residual stress
7. Tutorial of seminar project
8. Solution of contact problem by FEM
9. Tutorial of seminar project
10. Solution of large displacement problem by FEM
11. Solution of stability of shell
12. Example of an explicit FEM solver
13. Presentation of seminar projects